Question

1 ) 3 1/9 : 2 1/3 - 2 5/62) 1 5/7 - 4 3/13 : 1 19/26

Answer 1

1) 3 1/9:2 1/3=28/9:7/3=28/9*3/7=4/3=1 1/3

1 1/3-2 5/6=1 2/6-2 5/6=-1 3/6=-1 1/2

2) 4 3/13:1 19/26=55/13:45/26=55/13*26/45=22/9

1 5/7-22/9=12/7-22/9=108/63-154/63=-46/63

Answer 2

1.

3 1/9 : 2 1/3 - 2 5/6 = 28/9 : 7/3 - 17/6 =

= 28/9 * 3/7 - 17/6 = 4/3 - 17/6 =

= 8/6 - 17/6 = - 9/6 = - 3/2 = - 1 1/2,

или:

1) 3 1/9 : 2 1/3 = 28/9 : 7/3 = 28/9 * 3/7 = 4/3 = 1 1/3,

2) 1 1/3 - 2 5/6 = 4/3 - 17/6 = 8/6 - 17/6 = - 9/6 = - 3/2 = - 1 1/2,

2.

1 5/7 - 4 3/13 : 1 19/26 = 12/7 - 55/13 : 45/26 =

= 12/7 - 55/13 * 26/45 = 12/7 - 22/9 =

= 108/63 - 154/63 = - 46/63,

или:

1) 4 3/13 : 1 19/26 = 55/13 : 45/26 = 55/13 * 26/45 = 22/9 = 2 4/9,

2) 1 5/7 - 2 4/9 = 12/7 - 22/9 = 108/63 - 154/63 = - 46/63

Answer 3

To solve these expressions, we'll perform the operations step by step:

1. $\frac{3 \frac{1}{9}}{2 \frac{1}{3}} - 2 \frac{5}{62}$

Step 1: Convert mixed fractions to improper fractions: $3 \frac{1}{9} = \frac{(3 \times 9) + 1}{9} = \frac{28}{9}$ $2 \frac{1}{3} = \frac{(2 \times 3) + 1}{3} = \frac{7}{3}$

Step 2: Perform the division operation: $\frac{\frac{28}{9}}{\frac{7}{3}} = \frac{28}{9} \times \frac{3}{7} = \frac{28 \times 3}{9 \times 7} = \frac{84}{63} = \frac{4}{3}$

Step 3: Convert $2 \frac{5}{62}$ to an improper fraction: $2 \frac{5}{62} = \frac{(2 \times 62) + 5}{62} = \frac{129}{62}$

Step 4: Perform the subtraction operation: $\frac{4}{3} - \frac{129}{62}$

Now, we need to find a common denominator to subtract these fractions. The common denominator is the least common multiple (LCM) of 3 and 62, which is 186.

Step 5: Convert both fractions to have a denominator of 186: $\frac{4}{3} = \frac{4 \times 62}{3 \times 62} = \frac{248}{186}$ $\frac{129}{62} = \frac{129 \times 3}{62 \times 3} = \frac{387}{186}$

Step 6: Perform the subtraction: $\frac{248}{186} - \frac{387}{186} = \frac{248 - 387}{186} = \frac{-139}{186}$

So, the result of the first expression is $-\frac{139}{186}$.

2. $1 \frac{5}{7} - 4 \frac{3}{13} : 1 \frac{19}{26}$

Step 1: Convert mixed fractions to improper fractions: $1 \frac{5}{7} = \frac{(1 \times 7) + 5}{7} = \frac{12}{7}$ $4 \frac{3}{13} = \frac{(4 \times 13) + 3}{13} = \frac{55}{13}$

Step 2: Perform the division operation: $\frac{55}{13} : \frac{45}{26}$

To divide fractions, we take the reciprocal of the second fraction and multiply them: $\frac{55}{13} \times \frac{26}{45} = \frac{55 \times 26}{13 \times 45} = \frac{1430}{585}$